Optical element, method of manufacturing optical element, illumination device, window member, and fitting

ABSTRACT

An optical element includes a first surface, a second surface positioned to face the first surface, and a plurality of reflecting surfaces arrayed in a first region defined by the first surface and the second surface, wherein the reflecting surfaces have a first length in a first direction vertical to the first surface and are arrayed at a pitch in a second direction perpendicular to the first direction, light incident on one of the first surface and the second surface is reflected by the reflecting surfaces toward the other surface, and predetermined parameters satisfy predetermined relational formulae representing conditions for ensuring total reflection at the reflecting surfaces and for avoiding total reflection at a light emergent surface.

CROSS REFERENCES TO RELATED APPLICATIONS

The present application claims priority to Japanese Priority PatentApplication JP 2010-178947 filed in the Japan Patent Office on Aug. 9,2010, the entire contents of which are hereby incorporated by reference.

BACKGROUND

The present technology relates to an optical element that is used in acollector for collecting the sunlight or artificial light. The presenttechnology also relates to a method of manufacturing the opticalelement, an illumination device, a window member, and a fitting.

Recently, sunlight collectors have been developed with the view ofreducing electric power consumed by lighting apparatuses, when they areused in the daytime, by taking in the sunlight incoming from the skytoward the ceiling inside a house or a building. Various types ofstructures, e.g., a light duct, a louver, and a window blind (shade),are employed as related-art sunlight collectors.

For example, Japanese Unexamined Patent Application Publication(Translation of PCT Application) No. 2002-526906 describes an opticalcomponent for causing incident light to be directionally output byutilizing total reflection generated at a gap (space) that is formedinside an optically transparent body. Japanese Unexamined PatentApplication Publication No. 2009-266794 describes a sunlight illuminatorincluding a plurality of bar-shaped element members made of atransparent material, and a support for supporting the plural elementmembers such that the element members are arrayed parallel to eachother. In the sunlight illuminator, the sunlight incoming from theoutdoor side is reflected by reflecting surfaces of the element membersto be introduced toward the ceiling in the indoor side. Japanese PatentNo. 3513531 describes a sunlight collector for causing incident light tobe diffusively output through bar-like members, which are arrayed on thesurface of a transparent body in the form of a flat plate. JapaneseUnexamined Patent Application Publication No. 2001-503190 describes anoptical guide plate in which, in a plate made of a transparent plastichaving a first refractive index, a plurality of thin belt-like membersmade of a plastic having a second refractive index are inserted suchthat incident light is directionally output due to the difference inrefractive index between the plate and the belt-like members.

SUMMARY

In the field of the sunlight collector, an increase in efficiency oftaking in the sunlight or in efficiency of outputting the sunlightupward is desired. With the structures described in the above-citedpatent documents, however, the sunlight collector is to be larger inthickness for directionally outputting the incident light with highefficiency. In other words, there has been a difficulty in constructingthe sunlight collector in the form of a thin film.

Thus, it is desirable to provide an optical element, which can increasethe efficiency of taking in light and which is adaptable for a reductionof an element thickness. It is also desirable to provide a method ofmanufacturing the optical element, an illumination device, a windowmember, and a fitting.

The inventors have conducted intensive studies with intent to overcomethe above-mentioned problems in the related art. As a result, theinventors have found an optical element and an illumination device, theoptical element including a structure layer that has a plurality ofreflecting surfaces and that satisfies a predetermined relationshipamong a length of each of the plural reflecting surfaces in aone-dimensional direction, an array pitch of the plural reflectingsurfaces, and an incident angle of incident light.

For the reason in the manufacturing process, however, the structurelayer is often deviated (deformed) from the shape as per design values.The deviation of the shape of the reflecting surfaces from that as perthe design values adversely affects expected optical characteristics.

In view of the above-mentioned problem, the inventors have conductedintensive studies with intent to obtain the desired opticalcharacteristics even when the shape of the reflecting surfaces isdeviated from that as per the design values. As a result, the inventorshave found an optical element in which the shape of the reflectingsurfaces is designed to satisfy predetermined relational formulae byquantitatively evaluating the relationships between the deviations fromthe shape as per the design values and the optical characteristics.Further, the inventors have found a method of manufacturing the opticalelement, an illumination device, a window member, and a fitting, thelatter threes each employing the optical element.

According to one embodiment, an optical element includes a firstsurface, a second surface positioned to face the first surface, and aplurality of reflecting surfaces arrayed in a first region defined bythe first surface and the second surface, wherein the reflectingsurfaces have a first length in a first direction vertical to the firstsurface and are arrayed at a pitch in a second direction perpendicularto the first direction, light incident on one of the first surface andthe second surface is reflected by the reflecting surfaces toward theother surface, and following formulae (1) and (9) are satisfied:

$\begin{matrix}{d = {( {{2n} - 1} )\frac{p}{\tan \; \beta}( {n \in N} )}} & (1) \\{{( {n_{p} + {n_{air}\sin \; \alpha}} )( {n_{p} - {n_{air}\sin \; \alpha}} )\sin^{2}2\; \psi} \leq {n_{air}^{2}( {1 - {\cos \; 2{\psi sin}\; \alpha}} )}^{2}} & (9)\end{matrix}$

(where d is the first length, n is a number of total reflections of theincident light at the same reflecting surface, p is an array pitch ofthe reflecting surfaces, β is an angle formed between a projection ofthe light impinging on the reflecting surface to a surface including thefirst and second directions and a tangential line at an arbitrary pointon the reflecting surface) (6.5°≦β≦87.5°), N is a set of naturalnumbers, n_(p) is a refractive index inside the region defined by thefirst surface and the second surface, n_(air) is a refractive index ofair, α is an incidence angle of the light incident on the opticalelement, and ψ is an angle formed in the surface including the first andsecond directions between a tangential line at an arbitrary point on thereflecting surface and the first direction).

According to another embodiment, an optical element includes a firstsurface, a second surface positioned to face the first surface, and aplurality of reflecting surfaces arrayed in a first region defined bythe first surface and the second surface, wherein the reflectingsurfaces have a curvature in at least a portion thereof, have a firstlength in a first direction vertical to the first surface, and arearrayed at a pitch in a second direction perpendicular to the firstdirection, light incident on one of the first surface and the secondsurface is reflected by the reflecting surfaces toward the othersurface, and following formulae (1) and (16) are satisfied:

$\begin{matrix}{d = {( {{2n} - 1} )\frac{p}{\tan \; \beta}( {n \in N} )}} & (1) \\{( {\beta + \xi} ) \leq {{Arccos}( {- \; \frac{n_{air}}{n_{p\;}}} )}} & (16)\end{matrix}$

(where d is the first length, n is a number of total reflections of theincident light at the same reflecting surface, p is an array pitch ofthe reflecting surfaces, β is an angle formed between a projection ofthe light impinging on the reflecting surface to a surface including thefirst and second directions and a tangential line at an arbitrary pointon the reflecting surface) (6.5°≦β≦87.5°), N is a set of naturalnumbers, n_(p) is a refractive index inside the region defined by thefirst surface and the second surface, n_(air) is a refractive index ofair, and ξ is an angle of divergence of light diverging after beingfocused, the light impinging on the reflecting surface, when the portionof the reflecting surface having the curvature is regarded as a lens).

According to still another embodiment, an optical element includes afirst surface, a second surface positioned to face the first surface,and a plurality of reflecting surfaces arrayed in a first region definedby the first surface and the second surface, wherein the reflectingsurfaces have fine ruggedness, have a first length in a first directionvertical to the first surface, and are arrayed at a pitch in a seconddirection perpendicular to the first direction, light incident on one ofthe first surface and the second surface is reflected by the reflectingsurfaces toward the other surface, an energy distribution of the lightreflected by the reflecting surfaces is a Gaussian distribution with adirection of specular reflection being a center, a standard deviation ofthe Gaussian distribution is 5° or less, and a following formula (1) issatisfied:

$\begin{matrix}{d = {( {{2n} - 1} )\frac{p}{\tan \; \beta}( {n\; \in N} )}} & (1)\end{matrix}$

(where d is the first length, n is a number of total reflections of theincident light at the same reflecting surface, p is an array pitch ofthe reflecting surfaces, β is an angle formed between a projection ofthe light impinging on the reflecting surface to a surface including thefirst and second directions and a tangential line at an arbitrary pointon the reflecting surface) (6.5°≦β≦87.5°), and N is a set of naturalnumbers).

According to still another embodiment, a method of manufacturing anoptical element includes transferring a concave-convex shape formed in amaster to a transfer material, thereby forming a first lighttransmissive layer that has a plurality of reflecting surfaces in atransfer surface thereof, and joining the first light transmissive layerto a second light transmissive layer, wherein the reflecting surfaceshave a first length in a depth direction of the concave-convex shape ofthe transfer surface and are arrayed at a pitch in a second directionperpendicular to the depth direction of the concave-convex shape, lightincident on one principal surface of one of the first light transmissivelayer and the second light transmissive layer is reflected by thereflecting surfaces toward one principal surface of the other layer, andfollowing formulae (1) and (9) are satisfied:

$\begin{matrix}{d = {( {{2n} - 1} )\frac{p}{\tan \; \beta}( {n \in N} )}} & (1) \\{{( {n_{p} + {n_{air}\sin \; \alpha}} )( {n_{p} - {n_{air}\sin \; \alpha}} )\sin^{2}2\psi} \leq {n_{air}^{2}( {1 - {\cos \; 2\; {\psi sin}\; \alpha}} )}^{2}} & (9)\end{matrix}$

(where d is the first length, n is a number of total reflections of theincident light at the same reflecting surface, p is an array pitch ofthe reflecting surfaces, β is an angle formed between a projection ofthe light impinging on the reflecting surface to a surface including thefirst and second directions and a tangential line at an arbitrary pointon the reflecting surface (6.5°≦β≦87.5°), N is a set of natural numbers,n_(p) is a refractive index of the first light transmissive layer,n_(air) is a refractive index of air, α is an incidence angle of thelight incident on the optical element, and ψ is an angle formed in thesurface including the first and second directions between a tangentialline at an arbitrary point on the reflecting surface and the firstdirection).

According to still another embodiment, a method of manufacturing anoptical element includes transferring a concave-convex shape formed in amaster to a transfer material, thereby forming a first lighttransmissive layer that has a plurality of reflecting surfaces in atransfer surface thereof, and joining the first light transmissive layerto a second light transmissive layer, wherein the reflecting surfaceshave a curvature in at least a portion thereof, have a first length in adepth direction of the concave-convex shape of the transfer surface, andare arrayed at a pitch in a second direction perpendicular to the depthdirection of the concave-convex shape, light incident on one principalsurface of one of the first light transmissive layer and the secondlight transmissive layer is reflected by the reflecting surfaces towardone principal surface of the other layer, and following formulae (1) and(16) are satisfied:

$\begin{matrix}{d = {( {{2n} - 1} )\frac{p}{\tan \; \beta}( {n \in N} )}} & (1) \\{( {\beta + \xi} ) \leq {{Arccos}( {- \frac{n_{air}}{n_{p}}} )}} & (16)\end{matrix}$

(where d is the first length, n is a number of total reflections of theincident light at the same reflecting surface, p is an array pitch ofthe reflecting surfaces, β is an angle formed between a projection ofthe light impinging on the reflecting surface to a surface including thefirst and second directions and a tangential line at an arbitrary pointon the reflecting surface) (6.5°≦β≦87.5°), N is a set of naturalnumbers, n_(p) is a refractive index of the first light transmissivelayer, n_(air) is a refractive index of air, and ξ is an angle ofdivergence of light diverging after being focused, the light impingingon the reflecting surface, when the portion of the reflecting surfacehaving the curvature is regarded as a lens).

According to still another embodiment, a method of manufacturing anoptical element includes transferring a concave-convex shape formed in amaster to a transfer material, thereby forming a first lighttransmissive layer that has a plurality of reflecting surfaces in atransfer surface thereof, and joining the first light transmissive layerto a second light transmissive layer, wherein the reflecting surfaceshave fine ruggedness, have a first length in a depth direction of theconcave-convex shape of the transfer surface, and are arrayed at a pitchin a second direction perpendicular to the depth direction of theconcave-convex shape, light incident on one principal surface of one ofthe first light transmissive layer and the second light transmissivelayer is reflected by the reflecting surfaces toward one principalsurface of the other layer, and an energy distribution of the lightreflected by the reflecting surfaces is a Gaussian distribution with adirection of specular reflection being a center, a standard deviation ofthe Gaussian distribution is 5° or less, and a following formula (1) issatisfied:

$\begin{matrix}{d = {( {{2n} - 1} )\frac{p}{\tan \; \beta}( {n \in N} )}} & (1)\end{matrix}$

(where d is the first length, n is a number of total reflections of theincident light at the same reflecting surface, p is an array pitch ofthe reflecting surfaces, β is an angle formed between a projection ofthe light impinging on the reflecting surface to a surface including thefirst and second directions and a tangential line at an arbitrary pointon the reflecting surface) (6.5°≦β≦87.5°), and N is a set of naturalnumbers).

In some of the embodiments, the light incident on one of the firstsurface and the second surface is reflected by the reflecting surfacestoward the other surface. In the other embodiments, the light incidenton one principal surface of one of the first light transmissive layerand the second light transmissive layer is reflected by the reflectingsurfaces toward one principal surface of the other layer. The shape ofthe reflecting surfaces is designed to satisfy predetermined relationalformulae depending on the type of deviation of the shape of thereflecting surfaces from that as per design values. Therefore, even whenthe shape of a structure layer is deviated from that as per designvalues, the light incident on the optical element in a predeterminedangle range can be efficiently output in a predetermined angle range.Herein, the term “shape as per design values” implies the shapeobtained, for example, as follows. When the structure layer isconstituted by a plurality of structure units each to be formed in arectangular shape, the structure unit has an ideal rectangular shapefree from distortions.

With the embodiments, even when the shape of the structure layer isdeviated from that as per design values, the desired characteristics canbe obtained.

Additional features and advantages are described herein, and will beapparent from the following Detailed Description and the figures.

BRIEF DESCRIPTION OF THE FIGURES

FIG. 1 is a schematic perspective view illustrating an example in whichan optical element according to an embodiment is applied to a sunlightcollector;

FIG. 2 is a sectional view of an optical element according to a firstembodiment;

FIG. 3 is an illustration to explain the function of a reflectingsurface of the optical element;

FIG. 4 is an illustration to explain a variation in the amount ofemergent light output upwards depending on dimensional change of thereflecting surface;

FIG. 5 is an illustration to explain the relationship between athickness of the reflecting surface (width of a space (gap)) and anarray pitch of the reflecting surfaces;

FIG. 6 is an illustration to explain a variation in the amount ofemergent light output upwards depending on the thickness of thereflecting surface (width of the space);

FIGS. 7A to 7C are perspective views illustrating primary steps of oneexample of a method of manufacturing the optical element;

FIGS. 8A to 8F are schematic sectional views illustrating examples oftilting and curving of the shape of a structure layer;

FIGS. 9A to 9F are schematic sectional views illustrating examples oftilting and curving of the shape of the structure layer;

FIG. 10 is a schematic sectional view of principal part, the viewillustrating how light propagates through the interior of the opticalelement when the reflecting surface is inclined upwards to the emergent(output) side;

FIGS. 11A to 11C are schematic partial sectional views each illustratinga region in the vicinity of the space when the reflecting surface isinclined downwards to the emergent side;

FIGS. 12A to 12C are graphs to explain, when the shape of a distal endof a structure unit forming the structure layer is rounded, theinfluence of the rounding upon upward transmittance;

FIGS. 13A to 13C illustrate the simulation results to explain, when theshape of the distal end of the structure unit of the structure layer isrounded, the influence of the rounding upon upward transmittance;

FIGS. 14A to 14C are illustrations to explain the condition at whichdivergent light is totally reflected by the reflecting surface;

FIGS. 15A to 15C are illustrations to explain examples of a method forreducing the influence upon upward transmittance, which is caused by therounding of the shape of the distal end of the structure unit;

FIGS. 16A to 16C illustrate examples of a cross-section of the opticalelement when a first light transmissive layer and a second lighttransmissive layer are thermally welded or solvent-welded to each otherby a second or third method of reducing the influence of the roundingupon upward transmittance, which is caused by the rounding of the shapeof the distal end of the structure unit;

FIGS. 17A and 17B are illustrations to explain, when the surface of thestructure layer has fine ruggedness, the influence of the presence ofthe fine ruggedness upon upward transmittance;

FIG. 18 is an illustration to explain the shape of the structure layer,which is presumed in a simulation;

FIGS. 19A and 19B are graphs to explain the simulation results when anirradiation angle is set to 60°;

FIGS. 20A and 20B are graphs to explain the simulation results when theirradiation angle is set to 30°;

FIG. 21A is a graph plotting the results of simulations performed onstructure units forming structure layers that are used in TEST EXAMPLES1-1 to 1-3, and FIG. 21B is a graph plotting the results of simulationsperformed on structure units forming structure layers that are used inTEST EXAMPLES 1-4 to 1-7;

FIGS. 22A and 22B illustrate the simulation results representing areduction of the action of taking in light incident on the opticalelement with an increase of the curvature when the irradiation angle isset to 60°;

FIGS. 23A and 23B illustrate the simulation results representing areduction of the action of taking in light incident on the opticalelement with an increase of the curvature when the irradiation angle isset to 60°;

FIG. 24A is a graph plotting the results of simulations performed undera condition of σ=5° on structure units forming structure layers that areused in TEST EXAMPLES 2-1 to 2-3, and FIG. 24B is a graph plotting theresults of simulations under the condition of σ=5° performed onstructure units forming structure layers that are used in TEST EXAMPLES2-4 to 2-6;

FIGS. 25A and 25B illustrate an optical element according to a firstmodification;

FIG. 26 is a perspective view of an optical element according to asecond modification;

FIG. 27 illustrates a third modification;

FIG. 28A is a perspective view illustrating one example of theconstruction of a fitting that includes the optical element disposed ina lighting portion, and FIG. 28B is a sectional view illustrating oneexample of the construction of a lighting member;

FIG. 29A is a schematic view of an optical element including a structurelayer in which spaces are formed such that the distance between upperand lower surfaces defining each space, which are positioned to faceeach other, is continuously reduced from the light incident surface sidetoward the light emergent surface side, FIG. 29B is a schematic view ofan optical element having a structure in which a space providing upperand lower reflecting surfaces both inclined in the +Z-direction from thelight incident surface side toward the light emergent surface side and aspace providing upper and lower reflecting surfaces both inclined in the−Z-direction from the light incident surface side toward the lightemergent surface side are alternately arrayed in the Z-direction, andFIG. 29C is a schematic view of an optical element including spaces eachof which provides a reflecting surface inclined at a predeterminedinclination angle ψ with respect to an X-axis and a reflecting surfaceparallel to the X-axis direction;

FIGS. 30A to 30F illustrate other examples of the multilayer structureof the optical element; and

FIGS. 31A to 31D illustrate other examples of the multilayer structureof the optical element.

DETAILED DESCRIPTION

Embodiments of the present application will be described below in detailwith reference to the drawings.

1. First embodiment (in which the shape of a structure layer includestilting or curving)

2. Second embodiment (in which the shape of a distal end of a structureunit forming the structure layer is rounded)

3. Third embodiment (in which the surface of the structure layer hasfine ruggedness)

4. Modifications

1. First Embodiment

FIG. 1 is a schematic perspective view of the interior of a room, theview illustrating an example in which an optical element 1 according toan embodiment is applied to a window. The optical element 1 isconstituted as a sunlight collector for taking into a room R incidentlight L1 incoming from the outdoor, i.e., from the sun D. For example,the optical element 1 is used in the form of a window member for abuilding. The optical element 1 has the function of directionallyoutputting the incident light L1 incoming from the sky toward a ceilingC of the room R. The sunlight taken in toward the ceiling C isdiffusively reflected by the ceiling C to illuminate the interior of theroom R. Thus, because the sunlight is utilized for lighting in the room,electric power consumed by an illumination device IL in the daytime canbe reduced.

Basic Construction of Optical Element

FIG. 2 is a schematic sectional view illustrating the construction ofthe optical element 1. The optical element 1 has a multilayer structureincluding a first light transmissive layer 3, a second lighttransmissive layer 5, and a base 11. In FIG. 2, an X-axis directionrepresents the direction of thickness of the optical element 1, i.e.,the direction perpendicular to a light incident surface S1. A Y-axisdirection represents the horizontal direction in the surface of theoptical element 1, and a Z-axis direction represents the vertical (upand down) direction in the surface of the optical element 1.

The first light transmissive layer 3 contains, e.g., a material havingtransparency as a primary constituent. Examples of the material of thefirst light transmissive layer 3 include Triacetylcellulose (TAC),Polyester (Thermoplastic Polyester Elastomer (TPEE)),Polyethyleneterephtalate (PET), Polyimide (PI), Polyamide (PA), aramid,Polyethylene (PE), polyacrylate, polyethersulfone, polysulfone,Polypropylene (PP), diacetyl cellulose, polyvinyl chloride, acryl resin(Polymethylmethacrylate (PMMA), Polycarbonate (PC), epoxy resin, urearesin, urethane resin, and melamine resin. However, materials of thefirst light transmissive layer 3 are not limited to the above-mentionedexamples.

The second light transmissive layer 5 includes a structure layer 15(described in detail later) formed in one surface 15 a of the opticalelement 1, which is positioned to face the first light transmissivelayer 3. The structure layer 15 having good shape accuracy can be formedby using a resin material that has an excellent shape transfer property.Examples of the resin material having an excellent shape transferproperty include a thermoplastic resin, a thermosetting resin, and anenergy-ray curable resin composition, e.g., an ultraviolet curableresin. In this specification, the term “energy-ray curable resincomposition” implies a resin composition capable of being cured uponirradiation with an energy ray. Also, the term “energy ray” impliessuitable one of energy rays represented by an ultraviolet ray, a visibleray, etc.

The surface 15 a of the second light transmissive layer 5 is bonded tothe first light transmissive layer 3 with, for example, a transparentbonding layer 7 interposed therebetween. A transparent layer 21including the structure layer 15 is thereby formed. Thus, thetransparent layer 21 is made up of the first light transmissive layer 3,the second light transmissive layer 5, and the bonding layer 7. Be itnoted that the term “bonding layer” used in this specification includesan adhesive layer.

The second light transmissive layer 5 contains, e.g., a material havingtransparency as a primary constituent. While the second lighttransmissive layer 5 may be made of the same type of resin material asthat of the first light transmissive layer 3, the second lighttransmissive layer 5 preferably contains an ultraviolet curable resin asa primary constituent. Alternatively, the second light transmissivelayer 5 may be made of glass.

The ultraviolet curable resin contains, for example, (meth)acrylate anda photopolymerization initiator. The ultraviolet curable resin mayfurther contain, where necessary, a photo-stabilizer, a flame retardant,a leveling agent, a releasing agent, an anti-oxidant, etc. As theacrylate, a monomer and/or an oligomer having two or more (meth)acryloylgroups can be used. Examples of such a monomer and/or oligomer includeurethane(meth)acrylate, epoxy(meth)acrylate, polyester(meth)acrylate,polyol(meth)acrylate, polyether(meth)acrylate, andmelamine(meth)acrylate. Herein, the term “(meth)acryloyl group” impliesan acryloyl group or a methacryloyl group. The term “oligomer” usedherein implies a molecule having molecular weight of 500 or more to 6000or less. As the photopolymerization initiator, for example, abenzophenone derivative, an acetophenone derivative, or an anthraquinonederivative can be used alone or in combination.

Examples of the thermoplastic resin include polymethyl methacrylate,polyester resin, polyimide resin, polycarbonate resin, polyolefin resin,polystyrene resin, polyvinyl resin, polyacetal resin, melamine resin,and nylon resin.

Examples of the thermosetting resin include epoxy resin, polyurethaneresin, unsaturated polyester resin, phenol resin, and silicone resin.Any type of resin used here is preferably made of a material having hightransparency.

The base 11 is formed of a light transmissive resin film that is stacked(laminated) on the other surface 15 b (second surface) of the secondlight transmissive layer 5. The base 11 serves also as a protectivelayer and contains, e.g., a transparent material as a primaryconstituent. For example, the base 11 is made of the same type of resinmaterial as that of the first light transmissive layer 3. The base 11may be stacked on an outer surface of the first light transmissive layer3 as well in addition to the outer surface of the second lighttransmissive layer 5.

The optical element 1 having the above-described multilayer structure isstacked on the indoor side of a window member F. The window member F ismade of glass. The type of glass used as the window member F is notlimited to particular one. For example, a float plate glass, a laminatedglass, or a security glass can be employed. In the optical element 1according to the embodiment, the outer surface of the first lighttransmissive layer 3 is formed as the light incident surface S1, and anouter surface of the base 11 is formed as a light emergent surface S2.Be it noted that the base 11 can be omitted depending on situations. Insuch a case, the surface 15 b of the second light transmissive layer 5is preferably formed as the light emergent surface S2.

Structure Layer

The structure layer 15 will be described in detail below.

The structure layer 15 has a periodic structure of spaces (gaps) 151that are arrayed at a predetermined pitch in the up-and-down direction(Z-direction). Each of the spaces 151 has a depth d (first length) inthe X-axis direction (first direction) and a width w (second length) inthe Z-axis direction (second direction), and the spaces 151 are formedat an array pitch p in the Z-axis direction. Further, each space 151 isformed linearly in the Y-axis direction.

In FIG. 2, a surface defining each space 151 on the upper side forms areflecting surface 151 r that reflects the incident light L1 incomingthrough the light incident surface S1 toward the light emergent surfaceS2. Stated another way, the reflecting surface 151 r is formed by theinterface between a resin material (first medium) constituting thesecond light transmissive layer 5 and air (second medium) in the space151. In one embodiment, the relative refractive index of the secondlight transmissive layer 5 is set to, e.g., 1.3 to 1.7, thus providing adifference in refractive index between the second light transmissivelayer 5 and the air (refractive index of 1) in the space 151. Be itnoted that the second medium is not limited to air. For example, thereflecting surface 151 r may be formed by filling, in the space 151, amaterial having a lower refractive index than the second lighttransmissive layer 5.

FIG. 3 is an illustration to explain the function of the reflectingsurface 151 r. The reflecting surface 151 r produces emergent light L2,which is output upwards, by totally reflecting the incident light L1impinging on the reflecting surface 151 r from above. The expression“upwards” used in this specification implies directions at which anemergence (output) angle θ_(out) (FIG. 2) of the emergent light L2output from the light emergent surface S2 is 0° or more to 90° or less.While the following description is made in connection with the casewhere the light emergence direction is upward, the optical layout is notlimited to such an example. The light emergence direction may be changeddepending on, e.g., the light incidence (input) direction and theinstalled orientation of the optical element.

As illustrated in FIG. 3, it is defined that a length of the reflectingsurface 151 r in the X-axis direction is d, an array pitch of thereflecting surfaces 151 r is p, and an angle formed between a projectionof the light impinging on the reflecting surface 151 r to the XZ-planeand the X-axis is β. Further, in the following description, an angleformed between a contour line of the reflecting surface 151 r in itsXZ-section and the projection of the light impinging on the reflectingsurface 151 r to the XZ-plane is called an “irradiation angle” wherenecessary. When the reflecting surface 151 r has a curvature, the angleβ is given by drawing a tangential line with respect to the contour lineof the reflecting surface 151 r in its XZ-section, and by taking anangle formed between the tangential line and the projection of the lightimpinging on the reflecting surface 151 r to the XZ-plane. In theexample illustrated in FIG. 3, the angle β corresponds to theirradiation angle. Herein, the incident light L1 is totally reflected atthe reflecting surface 151 r when the following formula (1) issatisfied. In the example illustrated in FIG. 3, the incident lightimpinging on the reflecting surface 151 r at the irradiation angle β isall output upwards at the angle β.

$\begin{matrix}{d = {( {{2n} - 1} )\frac{p}{\tan \; \beta}( {n \in N} )}} & (1)\end{matrix}$

In the formula (1), n is a natural number and represents the number oftotal reflections of the incident light L1 at the same reflectingsurface 151 r.

In the optical element 1 according to the embodiment, the length d ofthe reflecting surface 151 r in the X-axis direction and the array pitchp of the reflecting surfaces 151 r are set to satisfy the formula (1) atany value of the irradiation angle β within a predetermined angle range.The angle satisfying the formula (1) will be referred to as a “settingirradiation angle” hereinafter.

In the formula (1), the amount of the emergent light L2 output upwardscan be replaced with an output width T of the emergent light L2 asillustrated in FIG. 3. With such a replacement, the amount (T(β)) of theemergent light L2 is expressed by the following formula (2) using theangle β formed between the incident light L1 and the X-axis in theXZ-plane and the array pitch p of the reflecting surfaces 151 r:

$\begin{matrix}{{T(\beta)} = \frac{p}{\tan \; \beta}} & (2)\end{matrix}$

On the other hand, when the incident light L1 impinges on the reflectingsurface 151 r at an angle differing from the setting irradiation angle,the amount of the emergent light L2 output upwards is reduced. Whenconsidering the amount of the emergent light, change in the irradiationangle with respect to the reflecting surface 151 r can be regarded aschange in the length d of the reflecting surface 151 r in the X-axisdirection. FIG. 4 is an illustration to explain a variation in theamount of light output upwards when the length of the reflecting surface151 r in the X-axis direction is increased by x. As seen from FIG. 4,the amount (T(x)) of emergent light output upwards when the length ofthe reflecting surface 151 r in the X-axis direction is increased by xis expressed by the following formula (3):

$\begin{matrix}{{T(x)} = {\frac{p}{\tan \; \beta} - x}} & (3)\end{matrix}$

An increase of the length of the reflecting surface 151 r in the X-axisdirection causes multiple reflections of light between the adjacentreflecting surfaces, thereby increasing light L3 reflected downwards. Inthe example illustrated in FIG. 4, therefore, a ratio of the emergentlight amount (T(x)) to the amount (T(β)) of the emergent light outputupwards at the setting irradiation angle is expressed by the followingformula (4):

$\begin{matrix}\begin{matrix}{T = {( {\frac{p}{\tan \; \beta} - x} )/\frac{p}{\tan \; \beta}}} \\{= ( {1 - {\frac{\tan \; \beta}{p}x}} )}\end{matrix} & (4)\end{matrix}$

As described above, the amount of light reflected by the reflectingsurface 151 r and output upwards is changed depending on change of theincidence (input) angle from the setting irradiation angle, and theemergent light amount is reduced in a larger amount at a larger changefrom the setting irradiation angle. Accordingly, the setting irradiationangle is optionally set depending on the use and the range ofirradiation angle of the light impinging on the reflecting surface 151r, taking into consideration an output loss caused by the change fromthe setting irradiation angle. Further, the setting irradiation angle isoptimized depending on the amount of light to be output upwards. Forexample, when the optical element 1 is used as a sunlight collector, thesetting irradiation angle can be set depending on, e.g., the range ofincidence angle of the sunlight in a local region, a season or a timezone where the collected light is utilized, and the illumination rangeof the emergent light having been collected.

In one embodiment, the reflecting surface 151 r is formed such that thesetting irradiation angle falls within the range of, for example, 6.5°or more to 87.5° or less. A lower limit of the range, i.e., 6.5°,corresponds to the altitude of the sun at the winter solstice innorthern Europe (e.g., at Oslo in Norway), and an upper limit of therange, i.e., 87.5°, corresponds to the altitude of the sun at the summersolstice at Naha in Okinawa (Japan). For example, the settingirradiation angle is set to about 60°. With such setting, the opticalelement 1 can efficiently take in the sunlight throughout the year inany region over the world. Further, the optical element 1 can greatlycontribute to reducing electric power consumed by an illumination devicein the daytime. The length d of the reflecting surface 151 r in theX-axis direction and the array pitch p of the reflecting surfaces 151 rcan be set as appropriate depending on the thickness (dimension in theX-axis direction) of the optical element 1. The length d and the arraypitch p are optimized, for example, in respective ranges of d=10 to 1000μm and p=100 to 800 μm.

An aperture ratio of the structure layer 13 will be described below.

The reflecting surfaces 151 r arranged as illustrated in FIG. 2 are eachformed as a surface defining the space 151 that has a width w in theZ-axis direction. Accordingly, the substantial array pitch of thereflecting surfaces 151 r in the optical element 1 according to theembodiment is affected by a value of the width w of the space 151. FIG.5 illustrates the relationship between the array pitch p of thereflecting surfaces 151 r and the width w of the space 151. Asillustrated in FIG. 5, an effective array pitch of the reflectingsurfaces 151 r is expressed by the following formula (5):

$\begin{matrix}{{AR} = \frac{p - w}{p}} & (5)\end{matrix}$

In the formula (5), AR represents the aperture ratio of the structurelayer 15. When the aperture ratio is small, an output proportion of theincident light is reduced and visibility through the optical element issignificantly degraded. FIG. 6 is an illustration to explain a reductionin the output amount of the incident light L1 depending on the width wof the space 151. As illustrated in FIG. 6, the incident light L1 goingto impinge on the reflecting surface 151 r is intercepted by an amountcorresponding to the width w of the space 151. Accordingly, inconsideration of the width w of the space 151, the amount of theincident light L1 impinging on the reflecting surface 151 r is expressedby the above-mentioned formula (5). By combining the formula (5) withthe above-mentioned formula (4), a proportion of the component of theincident light L1, which is output upwards, is expressed by thefollowing formula (6):

$\begin{matrix}{T = {( {1 - {\frac{\tan \; \beta}{p}x}} )( \frac{p - w}{p} )}} & (6)\end{matrix}$

In the embodiment, the width w of the space 151 is set to, e.g., 0.1 μmor more, and an upper limit of the width w is determined, for example,depending on a value of the array pitch p of the reflecting surfaces 151r. Further, the aperture ratio AR of the structure layer 15 is set to0.2 or more so that the light output upwards can be effectively takenout.

Method of Manufacturing Optical Element

A method of manufacturing the optical element 1 having theabove-described construction will be described below. FIGS. 7A to 7C areperspective views illustrating primary steps of one example of themethod of manufacturing the optical element 1 according to theembodiment.

First, as illustrated in FIG. 7A, a master 105 used for fabricating thesecond light transmissive layer 5 is prepared. The master 105 isconstituted as a metal die or a resin die, for example. A concave-convexshape 115 corresponding to the shape of the structure layer 15 is formedin one surface of the master 105. Then, as illustrated in FIG. 7B, thesecond light transmissive layer 5 having the structure layer 15 isformed by transferring the concave-convex shape 115 of the master 105 toa transfer material.

The transfer material can be, for example, an energy-ray curable resincomposition, or a resin sheet or a resin film including an energy-raycurable resin composition coated thereon. The energy-ray curable resincomposition is preferably an ultraviolet curable resin.

In more detail, when the ultraviolet curable resin is used as thematerial of the second light transmissive layer 5, the second lighttransmissive layer 5 is fabricated by irradiating the ultravioletcurable resin, which is in a state sandwiched between the base 11 andthe master 105, with an ultraviolet ray through the base 11, forexample. In such a case, the base 11 is preferably made of a resinmaterial, such as PET, which has good transparency to an ultravioletray.

Further, the second light transmissive layer 5 may be continuouslyfabricated in a roll-to-roll manner. In such a case, the master 105 canbe formed in the shape of a roll, and the concave-convex shape of themaster 105 can be transferred to a transfer material by using a transferprocess.

The transfer process can be practiced, for example, as a method ofsupplying a belt-like resin sheet from a roll and transferring the shapeof a die to the belt-like resin sheet under application of heat andpressure (called a laminating transfer process). As another example, thetransfer process can be practiced as a method of coating an energy-raycurable resin composition, which is in a state not yet cured, over abelt-like resin film and irradiating the energy-ray curable resincomposition, which is in a state nipped between the belt-like resin filmand a roll-shaped master, with an energy ray, thereby curing theenergy-ray curable resin composition. Examples of the energy ray usablehere include an electron ray, an ultraviolet ray, a visible ray, a gammaray, and an electron ray. The ultraviolet ray is preferable from theviewpoint of production equipment.

Next, as illustrated in FIG. 7C, the second light transmissive layer 5is bonded to the first light transmissive layer 3 with, for example, thebonding layer 7 interposed therebetween. As a result, the opticalelement 1 illustrated in FIG. 2 is fabricated. The first lighttransmissive layer 3 and the second light transmissive layer 5 may bebonded by welding both the layers to each other under application ofheat and pressure or with the use of a chemical solvent.

According to the above-described manufacturing method, the opticalelement 1 including the structure layer 15 can be easily fabricated.Further, the thickness of the optical element 1 can be easily reduced toa value of 25 μm to 2500 μm, for example, without making theconcave-convex shape of the master complicated. Moreover, since the base11 is stacked to the second light transmissive layer 5, the opticalelement can be given with appropriate rigidity, whereby easiness inhandling and durability can be improved.

The optical element 1 fabricated as described above is usually employedby being affixed to the window member F, but it may be used alone.According to the embodiment, the incident light impinging on eachreflecting surface 151 r in the structure layer 15 from above within thepredetermined angle range can be output upwards from the light emergentsurface S2 with high efficiency. Thus, the sunlight can be efficientlytaken in toward the ceiling of a room by using the optical element 1 asa sunlight collector.

A distribution of the emergent light from the optical element can becontrolled by forming the structure layer inside the optical element asdescribed above. On that occasion, if the shape of the structure layeris deviated (deformed) from the shape as per design values, expectedoptical characteristics are not satisfied in many cases. In view of sucha situation, the inventors have conducted intensive studies and havesucceeded in designing the structure layer in a way satisfyingpredetermined relational formulae to obtain the expected opticalcharacteristics by classifying the deviations of the shape of thestructure layer and by quantitatively evaluating the relationshipsbetween the deviations of the shape of the structure layer and theoptical characteristics.

The following three factors regarding the deviations of the shape of thestructure layer from the shape as per design values adversely affect theoptical characteristics of the optical element 1:

-   -   Tilting and/or curving in the shape of the structure layer    -   Shape of a distal end of a structure unit constituting the        structure layer    -   Roughness of the surface of the structure layer

Those factors are generated for the reasons in the manufacturingprocess, for example, and it is difficult to completely prevent theoccurrence of those factors. Therefore, specifying an allowable rangefor the deviation is one effective method for obtaining the expectedoptical characteristics.

The optical element according to the first embodiment relates to anoptical element which can suppress a reduction of the amount of theemergent light output upwards even when the shape of the structure layerincludes tilting and/or curving. In the following description, aproportion of a component of the light, which is incident on the opticalelement and is output upwards with respect to the optical element, iscalled an “upward transmittance”.

FIGS. 8A to 8F and FIGS. 9A to 9F are schematic sectional viewsillustrating examples of tilting and curving of the shape of thestructure layer. In FIGS. 8A to 8F and FIGS. 9A to 9F, the bonding layer7 and the base 11 are omitted. FIGS. 8A, 8C and 8E illustrate examplesin which the space 151 is inclined upwards toward the emergent side.FIGS. 8B, 8D and 8F illustrate how the incident light is reflected bythe reflecting surface 151 r in the respective examples of FIGS. 8A, 8Cand 8E. In each of the examples illustrated in FIGS. 8C and 8E, thereflecting surface 151 r has a certain curvature. FIGS. 9A, 9C and 9Eillustrate examples in which the space 151 is inclined downwards towardthe emergent side. FIGS. 9B, 9D and 9F illustrate how the incident lightis reflected by the reflecting surface 151 r in the respective examplesof FIGS. 9A, 9C and 9E. In each of the examples illustrated in FIGS. 9Cand 9E, the reflecting surface 151 r has a certain curvature. WhileFIGS. 8A to 8F and FIGS. 9A to 9F illustrate the examples in each ofwhich the space 151 has such a cross-sectional shape that opposing sidesof the cross-sectional shape are substantially parallel to each other,the cross-sectional shape of the space 151 is not limited to theillustrated one. For example, the cross-sectional shape of the space 151may be variously modified into, e.g., a shape having a curvature only inone side, or a shape having opposing sides that are expanded outwards inoppositely away directions.

The following description is made with attention focused on the shape ofthe reflecting surface 151 r. It is premised that, in the followingdescription, the difference in refractive index between the first lighttransmissive layer 3 and the second light transmissive layer 5 is assmall as negligible. Also, even when the bonding layer 7 and the base 11are present at any position inside the optical element 1, the differencein refractive index between the first light transmissive layer 3 and thesecond light transmissive layer 5 is premised to be as small asnegligible.

The incident light L1 entering the optical element 1 is refracted at thelight incident surface S1 and is reflected by the reflecting surface 151r. The light reflected by the reflecting surface 151 r is refracted atthe light emergent surface S2 and is output to the outside of theoptical element 1. When the structure layer 15 includes tilting and/orcurving, the irradiation angle with respect to the reflecting surface151 r is deviated from the design value, and the amount of light outputupwards from the optical element 1 is changed. On that occasion, theamount of light output upwards is changed in different ways depending onwhether the space 151 is inclined upwards or downwards towards theemergent side.

Upward Inclination Towards Emergent Side

When the reflecting surface 151 r is inclined upwards toward theemergent side as illustrated in FIGS. 8A to 8F, an impingement anglewith respect to the light emergent surface S2, at which the lightimpinges on the light emergent surface S2 after being reflected by thereflecting surface 151 r, is deviated from the design value. Therefore,unintended total reflection is caused at the light emergent surface S2and the upward transmittance is reduced.

FIG. 10 is a schematic sectional view of principal part, the viewillustrating how light propagates through the interior of the opticalelement when the reflecting surface is inclined upwards toward theemergent side. In an example illustrated in FIG. 10, the reflectingsurface 151 r is inclined upwards by an angle ψ with respect to theX-axis. The angle ψ will be also referred to as an “inclination angle”hereinafter.

As illustrated in FIG. 10, the incident light L1 entering the opticalelement 1 at an incidence angle α is refracted at the light incidentsurface S1. A refraction angle at that time is defined as φ. The lightpropagating through the interior of the optical element 1 impinges onthe reflecting surface 151 r at the irradiation angle (φ+ψ) and advancesto the light emergent surface S2 after being reflected by the reflectingsurface 151 r. The light reaching the light emergent surface S2 isrefracted at the light emergent surface S2 and is output as the emergentlight L2 to the outside. At that time, an angle at which the lightimpinges on the light emergent surface S2 is (φ+2ψ).

For suppressing a reduction of the component of the light output to theoutside of the optical element 1, it is effective to prevent totalreflection at the light emergent surface S2. Because the angle at whichthe light impinges on the light emergent surface S2 is (φ+2ψ), acritical angle for the total reflection at the light emergent surface S2depends on the inclination angle ψ.

Given that the refractive index of air is n_(air) and the refractiveindex of the interior of the optical element 1 is n_(p), the followingformula (7) is held at the light incident surface S1. Further, giventhat an emergence (output) angle of the emergent light L2 from the lightemergent surface S2 is θ_(out), a condition for preventing the totalreflection at the light emergent surface S2 is expressed by thefollowing formula (8).

n _(air) sin α=n _(p) sin φ  (7)

n _(p) sin(φ+2ψ)≦n _(air)  (8)

From the formulae (7) and (8), the following formula (9) is obtained.

(n _(p) +n _(air) sin α)(n _(p) −n _(air) sin α)sin² 2ψ≦n _(air) ²(1−cos2ψ sin α)²  (9)

Accordingly, the total reflection at the light emergent surface S2 canbe prevented and the reduction of the upward transmittance can besuppressed by designing the optical element 1 to satisfy the formula (9)even when the shape of the structure layer is tilted.

Be it noted that the formula (9) is further applicable to the case wherethe sectional shape of the space 151 is curved. In such a case, theangle ψ is provided as an angle formed between the X-axis and one oftangential lines drawn to the contour line of the reflecting surface 151r in its XZ-section, which one has a maximum inclination with respect tothe X-axis.

Downward Inclination Toward Emergent Side

As illustrated in FIGS. 9A to 9F, when the reflecting surface 151 r isinclined downwards toward the emergent side, the reflection at thereflecting surface 151 r is affected in a similar manner to that in thecase where the area contributing to the reflection is reduced. Forexample, the incident light input from a direction forming a very smallangle with respect to the X-axis is not reflected by the reflectingsurface 151 r. Therefore, the amount of light reflected by thereflecting surface 151 r is reduced, and a component of the lightcorresponding to the reduction in the amount of the reflected light isoutput downwards with respect to the optical element 1.

FIGS. 11A to 11C are schematic partial sectional views each illustratinga region in the vicinity of the space when the reflecting surface isinclined downwards toward the emergent side. In an example illustratedin FIG. 11A, the reflecting surface 151 r is inclined downwards by theangle ψ with respect to the X-axis. In an example illustrated in FIG.11B, the reflecting surface 151 r is entirely inclined downwards whileit is curved to be convex upwards with a certain curvature. In anexample illustrated in FIG. 11C, a linear line connecting both ends ofthe reflecting surface 151 r on the light incident side and the lightemergent side is inclined by the angle ψ with respect to the X-axis whenviewed in the XZ-section. Further, in FIGS. 11A to 11C, an angle formedbetween the light impinging on the reflecting surface 151 r and theX-axis is defined as φ.

The case of FIGS. 11A and 11B and the case of FIG. 11C will beseparately discussed below. In the case of FIGS. 11A and 11B, aninclination of a tangential line at the end of the reflecting surface151 r on the light incident side is to be smaller than the angle formedbetween the light impinging on the reflecting surface 151 r and theX-axis when viewed in the XZ-section, in order to ensure that theincident light is reflected by the reflecting surface 151 r. Statedanother way, in the example illustrated in FIG. 11A, the optical element1 is to be designed such that the inclination angle ψ is smaller thanthe angle φ.

In the case of FIG. 11C, an inclination of the linear line connectingboth the ends of the reflecting surface 151 r on the light incident sideand the light emergent side is to be smaller than the angle formedbetween the light impinging on the reflecting surface 151 r and theX-axis when viewed in the XZ-section, in order to ensure that theincident light is reflected by the reflecting surface 151 r. Statedanother way, in the example illustrated in FIG. 11C, the optical element1 is to be designed such that the inclination angle ψ is smaller thanthe angle φ.

Thus, depending on tilting and/or curving in the shape of the structurelayer, the optical element 1 is designed such that the inclination ofthe tangential line at the end of the reflecting surface 151 r on thelight incident side is smaller than the angle formed between the lightimpinging on the reflecting surface 151 r and the X-axis. Alternatively,the optical element 1 is designed such that the inclination of thelinear line connecting both the ends of the reflecting surface 151 r onthe light incident side and the light emergent side is smaller than theangle formed between the light impinging on the reflecting surface 151 rand the X-axis. The first length d can be provided as a length of thecontour line of the reflecting surface 151 r in the XZ-plane. Bydesigning the optical element as described above, the incident light canbe surely reflected at the reflecting surface 151 r. In addition, thereduction of the upward transmittance can be suppressed by satisfyingthe condition that the light reflected by the reflecting surface 151 ris not totally reflected at the light emergent surface S2.

As seen from the above discussion, the optical element 1 is to bedesigned such that the tilting and/or the curving in the shape of thestructure layer is held within the range satisfying the foregoingformula (9). In this connection, by regarding the inclination angle ψ asan angle formed between a tangential line at an arbitrary point of thereflecting surface 151 r and the X-axis in the XZ-plane, the totalreflection at the light emergent surface S2 can be suppressed regardlessof whether the space 151 is inclined upwards or downwards toward theemergent side. As a result, the reduction of the upward transmittancecan be suppressed even when the shape of the structure layer includesthe tilting and/or the curving.

2. Second Embodiment

A second embodiment relates to an optical element in which the reductionin the amount of light output upwards with respect to the opticalelement can be suppressed even when the shape of a distal end of astructure unit forming the structure layer is rounded. Herein, theexpression “distal end of a structure unit” implies an apex portion ofthe structure unit projecting toward the light incident side.

FIGS. 12A to 12C and FIGS. 13A to 13C serve to explain, when the shapeof the distal end of the structure unit forming the structure layer isrounded, the influence of the rounding upon the upward transmittance.Simulations were performed by presuming distal end shapes, illustratedin FIGS. 12A to 12C, as examples of the shape of the distal end of thestructure unit forming the structure layer. The optical simulationsoftware (Light Tools) available from ORA (Optical Research Associates)was used to perform the simulations. The following description regardingthe simulations is made on the premise that the structure layer is notembedded in, e.g., a resin and light enters the optical element from thedistal end side of the structure unit.

FIGS. 13A to 13C illustrate the simulation results correspondingrespectively to the distal end shapes illustrated in FIGS. 12A to 12C.FIG. 13A represents the case where the shape of the distal end of thestructure unit is not rounded (i.e., the case where the distal end shapedoes not have a curvature). FIG. 13B represents the case where the shapeof the distal end of the structure unit has a curvature of 0.01, andFIG. 13C represents the case where the shape of the distal end of thestructure unit has a curvature of 0.02. As seen from FIGS. 13A to 13C,when the shape of the distal end is rounded, the distal end acts like alens such that light entering the structure layer is focused at a pseudofocal point and then diverges. Also, it is seen that the amount of lightreflected by the reflecting surface 151 r as per intended is reducedwith the focusing action, thus reducing the upward transmittance.Further, it is seen that the reduction of the upward transmittance ismore significant as the shape of the distal end is rounded to a largerextent. Hence, even when the light impinging on the reflecting surface151 r is reflected as divergent light, the influence of the rounding ofthe distal end shape upon the optical characteristics of the opticalelement 1 can be reduced by designing the optical element 1 so that mostof the divergent light satisfies the condition for the total reflectionat the reflecting surface 151 r.

FIGS. 14A to 14C are illustrations to explain the condition for causingthe divergent light to be totally reflected by the reflecting surface.FIG. 14A is a schematic sectional view of a part of the structure layer.As illustrated in FIG. 14A, light incident on the distal end of thestructure unit forming the structure layer at an incidence angle α isrefracted at the incident surface, and the refracted light advances tothe reflecting surface 151 r. Given that the light is refracted at arefraction angle β, the incidence angle α and the refraction angle βsatisfy the following formula (10):

n _(air) sin α=n _(p) sin β  (10)

Thus, the light refracted at the incident surface enters the reflectingsurface 151 r at the irradiation angle β. Total reflection occurs at thereflecting surface 151 r when the irradiation angle β satisfies thefollowing formula (11):

$\begin{matrix}{\beta \leq {{Arccos}( {- \frac{n_{air}}{n_{p}}} )}} & (11)\end{matrix}$

FIG. 14B is a schematic sectional view of the distal end of thestructure unit forming the structure layer. It is here premised that thedistal end of the structure unit has a width V in the Z-axis (seconddirection) and the shape of the distal end is rounded in the form of acircular arc having the radius R. Also, it is premised that the focalpoint is f when the rounded portion is regarded as a lens, and animaginary optical axis intersects the structure unit at points A and B.Given that divergence of the light diverging after being focused at thefocal point f is expressed by ξ, the irradiation angle with respect tothe reflecting surface 151 r is in the range of β to (β+ξ). In thefollowing description, the divergence ξ of the divergent light isreferred to as a “divergent angle ξ” for the convenience of explanation.

Consider now the relationship between the divergent angle ξ and theshape of the structure unit. As illustrated in FIG. 14C, end points ofthe circular arc are denoted by a and b, and the distance from a pointat which a linear line connecting the points a and b intersects animaginary optical axis AB to the focal point f is denoted by l₁. Thedistance from the focal point f to the point B is denoted by l₂. A pointat which a linear line drawn perpendicularly to the imaginary opticalaxis AB while passing the point B intersects a linear line connectingthe point a and the focal point f is denoted by d. A point at which alinear line drawn perpendicularly to the imaginary optical axis AB whilepassing the point B intersects a linear line connecting the point b andthe focal point f is denoted by c. On those definitions, a distance Dbetween the points c and d can be considered as representing a degree oflight divergence when the rounded portion in the shape of the distal endis regarded as a lens.

Because a triangle abf and a triangle dcf are similar to each other, thefollowing formula (12) is held:

$\begin{matrix}{\frac{\sqrt{2}R}{D} = \frac{l_{1}}{l_{2\;}}} & (12)\end{matrix}$

Here, the distance l₂ from the focal point f to the point B satisfiesthe following formula (13):

$\begin{matrix}\begin{matrix}{l_{2} = {\overset{\_}{AB} - \{ {l_{1} + {R( {1 - \frac{\sqrt{2}}{2}} )}} \}}} \\{= {{\sqrt{2}V} - l_{1} - {R( {1 - \frac{\sqrt{2}}{2}} )}}}\end{matrix} & (13)\end{matrix}$

From the formulae (12) and (13), the degree D of light divergence isexpressed by the following formula (14) using the radius R of thecircular arc aAb, the distance l₁, and the width V of the distal end ofthe structure unit in the Z-direction:

$\begin{matrix}{D = {\sqrt{2}R\{ {\frac{\sqrt{2}V}{l_{1}} - 1 - {\frac{R}{l_{1}}( {1 - \frac{\sqrt{2}}{2}} )}} \}}} & (14)\end{matrix}$

Accordingly, the divergent angle ξ of the light after being focused isexpressed by the following formula (15) using the degree D of lightdivergence in the formula (14):

$\begin{matrix}{\xi = {2{{Arctan}( \frac{D}{2l_{2}} )}}} & (15)\end{matrix}$

Here, the condition for causing the light impinging on the reflectingsurface 151 r at the irradiation angle β to be totally reflected by thereflecting surface 151 r is expressed by the foregoing formula (11).Further, when the rounded portion in the shape of the distal end isregarded as a lens, the irradiation angle of the light diverging afterbeing focused is in the range of β to (β+ξ) with respect to thereflecting surface 151 r. Therefore, it is understood that the conditionfor causing the divergent light to be totally reflected by thereflecting surface 151 r can be expressed by the following formula (16):

$\begin{matrix}{( {\beta + \xi} ) \leq {{Arccos}( {- \frac{n_{air}}{n_{p}}} )}} & (16)\end{matrix}$

From the formulae (10) and (11), the incidence angle α is desirablywithin the range expressed by the following formula (17):

$\begin{matrix}{\alpha \leq {{{Arcsin}( \frac{n_{p}}{n_{air}} )}{\sin ( {{Arccos}( {- \frac{n_{air}}{n_{p}}} )} )}}} & (17)\end{matrix}$

Thus, the optical element 1 is to be designed such that the conditionexpressed by the formula (17) is satisfied under the condition expressedby the formula (16). By designing the optical element 1 in such amanner, the reduction of the upward transmittance in the optical element1, which is attributable to the rounding of the distal end shape, can bereduced.

Optical Compensation for Rounding of Distal End Shape

The optical element according to the second embodiment can also beformed, as described above with reference to FIG. 7, by bonding onelight transmissive layer (second light transmissive layer 5), to whichthe concave-convex shape of the master has been transferred, to theother light transmissive layer (first light transmissive layer 3). Inother words, the bonding layer is arranged on the distal end side of thestructure unit forming the structure layer. Therefore, the influence ofthe rounding of the distal end shape upon the upward transmittance canbe reduced by improving the step of bonding the distal end of thestructure unit forming the second light transmissive layer, to which theconcave-convex shape of the master has been transferred, to the firstlight transmissive layer.

FIGS. 15A to 15C are illustrations to explain examples of a method forreducing the influence upon the upward transmittance, which is caused bythe rounding of the shape of the distal end of the structure unit. FIGS.15A to 15C correspond respectively to first to third methods forreducing the influence upon the upward transmittance.

According to the first method for reducing the influence upon the upwardtransmittance, the distal end of the structure unit and the first lighttransmissive layer are joined to each other with a bond or an adhesiveinterposed therebetween in such a state that at least a part of thedistal end of the structure unit is embedded in a joining layer made ofthe bond or the adhesive. Thus, the divergence of light caused by therounded portion of the distal end of the structure unit can be reducedby, as illustrated in FIG. 15A, embedding the rounded portion of thedistal end of the structure unit in the joining layer 37. In the exampleillustrated in FIG. 15A, because the bond or the adhesive is previouslyformed on one surface of a separator 39, the distal end of the structureunit can be embedded in the joining layer 37 by applying pressure to thejoining layer 37 through the separator 39. Alternatively, the distal endof the structure unit may be embedded in the joining layer 37 by peelingoff the separator 39 after attaching the distal end of the structureunit to the joining layer 37, and by applying pressure when the distalend of the structure unit and the first light transmissive layer arejoined to each other with the joining layer 37 interposed therebetween.In any of the above-mentioned cases, the difference in refractive indexbetween the material of the joining layer 37 and the material of thedistal end of the structure unit forming the structure layer ispreferably as small as possible.

According to the second method for reducing the influence upon theupward transmittance, a surface layer portion of the distal end of thestructure unit is processed to be swollen by a chemical solvent, and thedistal end of the structure unit and the first light transmissive layer3 are joined to each other under application of pressure. Thus, asillustrated in FIG. 15B, the distal end of the structure unit, which hasbeen swollen by the chemical solvent, is press-bonded to the first lighttransmissive layer 3. As a result, the rounded shape of the distal endof the structure unit is made closer to the shape as per the designvalues such that the parameters fall within the allowable ranges indesign, which are obtained through the above-described procedures, forexample.

The chemical solvent employed in the second method may be any type ofsolvent as long as, in basic properties, the chemical solvent is able todissolve the resin used. For example, the chemical solvent can beoptionally selected from among ketone-based solvents such as acetone,methylethylketone, and cyclohexanon, aromatic-based solvents such astoluene and xylene, ester-based solvents such as methyl acetate andethyl acetate, and hydrocarbon-based solvents (including linear, cyclic,and heterocyclic hydrocarbons, e.g., N-methylpyrrolidone). It ispreferable to employ the chemical solvent having a dissolution parameterclose to that of the resin used.

According to the third method for reducing the influence upon the upwardtransmittance, the distal end of the structure unit and the first lighttransmissive layer 3 are joined to each other under application of heatand pressure to the distal end of the structure unit. Thus, bypress-bonding the distal end of the structure unit to the first lighttransmissive layer 3 under application of heat H through the first lighttransmissive layer 3 as illustrated in FIG. 15C, the rounded shape ofthe distal end of the structure unit is made closer to the shape as perthe design values such that the parameters fall within the allowableranges in design, which are obtained through the above-describedprocedures, for example. As a result, a proportion of the roundedportion in the distal end of the structure unit can be reduced and thedivergence of light caused by the rounded portion of the distal end ofthe structure unit can also be reduced.

FIGS. 16A to 16C illustrate examples of a cross-section of the opticalelement when the first light transmissive layer 3 and the second lighttransmissive layer 5 are thermally welded or solvent-welded to eachother by the above-described second or third method. As one experimentalexample, the distal end of the structure unit forming the structurelayer, having the shape illustrated in FIG. 16A, and the first lighttransmissive layer 3 were joined to each other by using theabove-described second method. By observing a cross-section of theoptical element 1 obtained in such an example, it was confirmed that, asillustrated in FIG. 16B, an apex portion of the distal end of thestructure unit was welded to the first light transmissive layer and theinterface therebetween was not found. It is hence possible to reduce notonly the proportion of the rounded portion in the distal end of thestructure unit, but also the divergence of light caused by the roundedportion of the distal end of the structure unit. Further, whenoverpressure is applied in the thermal-welding or solvent-welding stepaccording to the second or third method, the obtained optical elementmay have a cross-section illustrated in FIG. 16C. Even in such a case,since the apex portion of the distal end of the structure unit is weldedto the first light transmissive layer and there exists no interfacetherebetween, the divergence of light caused by the rounded portion ofthe distal end of the structure unit can be reduced.

3. Third Embodiment

A third embodiment relates to an optical element in which the reductionin the amount of light output upwards with respect to the opticalelement can be suppressed even when the surface of the structure layerhas fine ruggedness.

FIGS. 17A and 17B are illustrations to explain, when the surface of thestructure layer has fine ruggedness, the influence of the presence ofthe fine ruggedness upon the upward transmittance. FIG. 17A is aschematic sectional view of a part of the structure layer. The surfaceof the structure layer of the optical element, i.e., the reflectingsurface 151 r, is ideally a smooth surface. In fact, however, thereflecting surface 151 r has fine ruggedness as illustrated in FIG. 17A.The fine ruggedness is generated, for example, through such a processthat fine ruggedness having been produced in the step of fabricating themaster is transferred to the reflecting surface 151 r.

The fine ruggedness of the reflecting surface 151 r may be substantiallyperiodic, but it is present at random with high probability. The fineruggedness of the reflecting surface 151 r diffusively reflects thelight impinging on the reflecting surface 151 r. It is therefore thoughtthat energy of the light reflected by the reflecting surface 151 rhaving the fine ruggedness is distributed in accordance with theGaussian distribution with the direction of specular reflection being ata center.

FIG. 17B illustrates the energy distribution of the light reflected bythe reflecting surface 151 r having the fine ruggedness. An angle θdenoted in FIG. 17B represents an angle that is measured with respect tothe direction of specular reflection in the XZ-plane. P(θ) representingthe luminosity or the radiance in the direction θ is expressed by thefollowing formula (18):

$\begin{matrix}{{P(\theta)} = {P_{0}{\exp \lbrack {- \frac{\theta^{2}}{2\sigma^{2}}} \rbrack}}} & (18)\end{matrix}$

In the above formula (18), P0 is the luminosity or the radiance in thedirection of specular reflection, and σ represents the standarddeviation of the Gaussian distribution. In the following description,the standard deviation σ is referred to as “surface roughness” for theconvenience of explanation.

The light reflected by the reflecting surface 151 r having the fineruggedness can be regarded as having the energy distribution representedby P(θ). Therefore, an impingement angle to the light emergent surfaceS2 at which the light impinges on the light emergent surface S2 afterbeing reflected by the reflecting surface 151 r has a certain variation.With such a variation, the light is unintentionally totally reflected atthe light emergent surface S2 depending on the impingement angle to thelight emergent surface S2, and the upward transmittance is reduced incomparison with the case where the reflecting surface 151 r is a smoothsurface.

To examine the influence of the fine ruggedness of the reflectingsurface upon the upward transmittance, simulations were performed on thepremise that the structure layer had the shape illustrated in FIGS. 18Aand 18B. The optical simulation software (Light Tools) available fromORA was used to perform the simulations.

FIG. 19A is a graph plotting transmittance T [%] with respect to theemergence (output) angle θout [°] when the irradiation angle is set to60°. The transmittance T at θout≧0° corresponds to the upwardtransmittance. In the graph of FIG. 19A, G1 to G5 represent respectivelythe simulation results at σ=0°, 0.5°, 1°, 3°, and 5°. FIG. 19B is agraph plotting relative upward transmittance Rr [%] with respect to thesurface roughness σ when the irradiation angle is set to 60°. FIG. 20Ais a graph plotting transmittance T [%] with respect to the emergenceangle θout [°] when the irradiation angle is set to 30°. In the graph ofFIG. 20A, G6 to G10 represent respectively the simulation results atσ=0°, 0.5°, 1°, 3°, and 5°. FIG. 20B is a graph plotting relative upwardtransmittance Rr [%] with respect to the surface roughness σ when theirradiation angle is set to 30°. Herein, the term “relative upwardtransmittance Rr [%]” implies a ratio of the upward transmittance ateach value of σ to the upward transmittance at σ=0°.

The following points are understood from the simulation results of FIGS.19A and 19B and FIGS. 20A and 20B. The surface roughness a satisfiespreferably σ≦5° and more preferably σ≦2.5°. When σ≦5° is satisfied, itcan be ensured that the relative upward transmittance is held at least1% or more. Further, when σ≦2.5° is satisfied, it can be ensured thatthe relative upward transmittance is held 10% or more. Even morepreferably, σ≦1° is satisfied. When σ≦1° is satisfied, it can be ensuredthat the relative upward transmittance is held 25% or more.

The surface roughness σ of the optical element can be estimated, forexample, as follows. First, arithmetic average ruggedness Ra is obtainedby cutting the optical element along the XZ-plane, and by observing thesectional shape of the reflecting surface 151 r. Then, a comparativesample of which Ra has been determined in advance is prepared and P(θ)of the comparative sample is measured by using a spectroscopicgoniometer. Alternatively, P(θ) is obtained through a simulation. Thus,σ at P(θ) of the comparative sample having Ra, of which value is closeto that of Ra obtained by observing the cross-section of the opticalelement, can be regarded as the surface roughness σ of the opticalelement.

Thus, when the surface of the structure layer has the fine ruggedness,the optical element 1 is to be designed such that the standard deviationof the energy distribution of the reflected light satisfies theabove-described condition. As a result, the reduction of the upwardtransmittance of the optical element 1 caused by the fine ruggedness ofthe reflecting surface can be suppressed.

EXAMPLES

The present technology will be described in more detail below inconnection with EXAMPLES, but the present technology is not limited tothe following EXAMPLES.

Test Example 1

In TEST EXAMPLE 1 described below, the influence upon the transmittancecaused by the rounding of the shape of the distal end of the structureunit forming the structure layer was determined through simulations. Thesimulations were performed on optical elements, described in thefollowing TEST EXAMPLES 1-1 to 1-7, by using the optical simulationsoftware (Light Tools) available from ORA. On the premise that therounded portion of the distal end of the structure unit was in the formof a circular arc, the transmittance T [%] was determined while thecurvature of the circular arc was changed.

Test Example 1-1

First, the structure unit forming the structure layer was premised to besimilar to that illustrated in FIGS. 14A and 14B. Further, it waspremised that the curvature was 0.01 and the irradiation angle was 0°.

Test Example 1-2

The structure unit forming the structure layer was premised as in TESTEXAMPLE 1-1 except that the curvature was set to 0.02.

Test Example 1-3

The structure unit forming the structure layer was premised as in TESTEXAMPLE 1-1 except that the curvature was set to 0.03.

Test Example 1-4

The structure unit forming the structure layer was premised as in TESTEXAMPLE 1-1 except that the shape of the distal end of the structureunit was not rounded (namely, it had no curvature) and the irradiationangle was set to 60°.

Test Example 1-5

The structure unit forming the structure layer was premised as in TESTEXAMPLE 1-1 except that the curvature was set to 0.01 and theirradiation angle was set to 60°.

Test Example 1-6

The structure unit forming the structure layer was premised as in TESTEXAMPLE 1-1 except that the curvature was set to 0.02 and theirradiation angle was set to 60°.

Test Example 1-7

The structure unit forming the structure layer was premised as in TESTEXAMPLE 1-1 except that the curvature was set to 0.03 and theirradiation angle was set to 60°.

FIG. 21A is a graph plotting the results of the simulations performed onthe structure units forming the structure layers, which are employed inTEST EXAMPLES 1-1 to 1-3. In the graph of FIG. 21A, R1 to R3 representrespectively the simulation results in TEST EXAMPLES 1-1, 1-2 and 1-3.Further, FIG. 21B is a graph plotting the results of the simulationsperformed on the structure units forming the structure layers, which areemployed in TEST EXAMPLES 1-4 to 1-7. In the graph of FIG. 21B, R4 to R7represent respectively the simulation results in TEST EXAMPLES 1-4, 1-5,1-6 and 1-7.

The following points are understood from FIGS. 21A and 21B. At theirradiation angle of 0°, as the curvature increases, a peak of thetransmittance lowers and the optical element exhibits a broader opticalcharacteristic. At the irradiation angle of 60°, as the curvatureincreases, both upward transmittance (θout≧0°) and downwardtransmittance (θout<0°) decrease. In other words, the action of takingin the light incident on the optical element is reduced. FIGS. 22A and22B and FIGS. 23A and 23B illustrate the simulation results representingthe reduction of the action of taking in the light incident on theoptical element with an increase of the curvature when the illuminationangle is set to 60°. FIG. 22A corresponds to the simulation result inTEST EXAMPLE 1-4, and FIG. 22B corresponds to the simulation result inTEST EXAMPLE 1-5. FIG. 23A corresponds to the simulation result in TESTEXAMPLE 1-6, and FIG. 23B corresponds to the simulation result in TESTEXAMPLE 1-7.

Test Example 2

In TEST EXAMPLE 2 described below, the influence upon the transmittancecaused by the fine ruggedness in the surface (reflecting surface) of thestructure unit forming the structure layer was determined throughsimulations. The simulations were performed on optical elements,described in the following TEST EXAMPLES 2-1 to 2-6, by using theoptical simulation software (Light Tools) available from ORA. For eachof the case where the reflecting surface had a scattering (diffusion)characteristic and the case where the reflecting surface had noscattering characteristic (σ=0°), the transmittance T [%] was determinedwhile the irradiation angle was changed.

Test Example 2-1

First, the structure unit forming the structure layer was premised to besimilar to that illustrated in FIGS. 18A and 18B. Further, it waspremised that the reflecting surface 151 r had a scatteringcharacteristic, namely, the reflected light had an energy distributionin accordance with the Gaussian distribution, and the irradiation anglewas 10°.

Test Example 2-2

The structure unit forming the structure layer was premised as in TESTEXAMPLE 2-1 except that the irradiation angle was set to 30°.

Test Example 2-3

The structure unit forming the structure layer was premised as in TESTEXAMPLE 2-1 except that the irradiation angle was set to 60°.

Test Example 2-4

The structure unit forming the structure layer was premised as in TESTEXAMPLE 2-1 except that the reflecting surface 151 r had no scatteringcharacteristic and the irradiation angle was set to 10°.

Test Example 2-5

The structure unit forming the structure layer was premised as in TESTEXAMPLE 2-1 except that the reflecting surface 151 r had no scatteringcharacteristic and the irradiation angle was set to 30°.

Test Example 2-6

The structure unit forming the structure layer was premised as in TESTEXAMPLE 2-1 except that the reflecting surface 151 r had no scatteringcharacteristic and the irradiation angle was set to 60°.

FIG. 24A is a graph plotting the results of the simulations performed onthe structure units forming the structure layers, which are employed inTEST EXAMPLES 2-1 to 2-3. In the graph of FIG. 24A, R8 to R10 representrespectively the simulation results in TEST EXAMPLES 2-1, 2-2 and 2-3under the condition of σ=5°. Further, FIG. 24B is a graph plotting theresults of the simulations performed on the structure units forming thestructure layers, which are employed in TEST EXAMPLES 2-4 to 2-6. In thegraph of FIG. 24B, R11 to R13 represent respectively the simulationresults in TEST EXAMPLES 2-4, 2-5 and 2-6 under the condition of σ=5°.

As understood from FIGS. 24A and 24B, when the reflecting surface 151 rhas the scattering characteristic, the upward transmittance is reducedin comparison with the case where the reflecting surface 151 r has noscattering characteristic. Further, the reduction of the upwardtransmittance is more significant at a larger irradiation angle.

4. Modifications

While the embodiments have been description in detail, the presenttechnology is not limited to the above-described embodiments, and it canbe variously modified on the basis of the technical concept.

First Modification

FIGS. 25A and 25B illustrate an optical element 201 according to a firstmodification.

The optical element 201 according to the first modification basicallyincludes a first light transmissive layer 203 and a second lighttransmissive layer 205. As illustrated in FIG. 25A, the first lighttransmissive layer 203 has an outer surface forming a light incidentsurface S1, and an inner surface in which a plurality of recesses 203 aare formed such that the recesses 203 a are each extended in the Y-axisdirection and are arrayed at a pitch in the Z-axis direction. On theother hand, the second light transmissive layer 205 has an outer surfaceforming a light emergent surface S2, and an inner surface in which aplurality of recesses 205 a are formed such that the recesses 205 a areeach extended in the Y-axis direction and are arrayed at a pitch in theZ-axis direction. Thus, the inner surfaces of the first lighttransmissive layer 203 and the second light transmissive layer 205include projections 203 b and projections 205 b, which are demarcated bythe recesses 203 a and the recesses 205 a, respectively. The projections203 b and 205 b are projected substantially parallel in the X-axisdirection and have the same projection length.

The optical element 201 according to the first modification isfabricated by arranging the first light transmissive layer 203 and thesecond light transmissive layer 205, as illustrated in FIG. 25B, intosuch a stacked structure that the projections 203 b or 205 b on onelayer are positioned at midpoints of the corresponding recesses 203 a or205 a on the other layer. As a result, a structure layer 215 is formedwhich includes a plurality of spaces 251 having the same shape andarrayed at a pitch in the Z-axis direction, the spaces 251 beingpositioned in the recesses 203 a and 205 a in a state sandwiched betweenthe projections 203 b and 205 b. Thus, the optical element 201 having atransparent layer 221, which includes the structure layer 215, isconstructed.

In the optical element 201 according to the first modification, areflecting surface for reflecting the sunlight is formed by a surfacedefining each space 251 on the upper side thereof. The depth, width, andarray pitch of the spaces 251 are set respectively depending on theheight, width, and array pitch of the projections 203 b and 205 b. Evenin the optical element 210 constructed as described above, advantageouseffects similar to those in the foregoing embodiments can also beobtained by applying the above-described design method in considerationof the deviation (deformation) of the shape of the structure layer.

The first light transmissive layer 203 and the second light transmissivelayer 205 can be each fabricated by using the master illustrated in FIG.7A. Both the light transmissive layers 203 and 205 may be joined to eachother by using, e.g., a transparent adhesive. Alternatively, when distalends of the projections 203 b and 205 b are rounded, both the lighttransmissive layers 203 and 205 may be joined to each other in a mannerof reducing the rounding by using one of the methods described abovewith reference to FIGS. 15A to 15C.

Second Modification

FIG. 26 is a perspective view of an optical element 301 according to asecond modification. The optical element 301 according to the secondmodification has a multilayer structure including a light transmissivelayer 305 including spaces 351 formed in one surface thereof, and aprism sheet 311 (second base) having a structure surface on which prisms311P are arrayed. The spaces 351 are formed in the one surface of thelight transmissive layer 305 on the light incident side, and the prisms311P are formed in the other surface of the light transmissive layer 305on the light emergent side. The prisms 311P are each formed with itsridgeline extending in the Z-axis direction and are arrayed at a pitchin the Y-axis direction.

In the optical element 301 constructed as described above, the ridgelinedirection of each prism 331P is aligned with the direction in which thespaces 351 are arrayed at a pitch (i.e., with the Z-axis direction).Therefore, incident light reflected by the surface defining each space351 on the upper side thereof (i.e., the reflecting surface) is outputfrom the optical element 301 such that emergent light is diffused(spread) in the Y-axis direction by the refractive action at slopedsurfaces of the prisms 311P when the light exits the prism sheet 311after passing through it. As a result, the function of outputting thelight, which has entered the optical element 301, upwards and thefunction of diffusing the incident light laterally can be obtained atthe same time.

Respective values of the array pitch, the height, the apex angle, etc.of the prisms 311P can be set as appropriate depending on the intendedlight output characteristic. Further, the incident light can beseparated into four directions, i.e., upwards, downwards, leftwards, andrightwards, by using the light transmissive layer 305 and the prismsheet 311.

The form of the prisms 311P is not limited to a periodic one, and theprisms 311P may be aperiodically formed in different sizes and/ordifferent shapes. Further, the prism sheet 311 may be arranged on thelight incident side of the light transmissive layer 305. In addition,the array direction of the prisms 311P is not limited to the Y-axisdirection as in the above-described construction, and it may be set toobliquely intersect the array direction of the spaces 351.

The base for diffusing (spreading) the light is not limited to the prismsheet described above, and it may also be practiced by using suitableone of various light transmissive films including light diffusingelements, which have periodic or aperiodic shapes, such as a crimpedfilm, a light transmissive film including striped crimps, and a lighttransmissive film including semispherical or cylindrical curved lensesformed on its surface. Further, a film having the same structure layeras that of the light transmissive layer 305 may be used as the lightdiffusing film. In that case, a degree of diffusing the light can beincreased by stacking the relevant film in such an orientation that thespace extending direction of the relevant film intersects the spaceextending direction of the light transmissive layer 305 positioned onthe light incident side.

Third Modification

FIG. 27 illustrates a third modification. An illumination device 400according to the third modification includes a luminous body 40, anadvertising medium 48, and a light transmissive film 405 arrangedbetween the luminous body 40 and the advertising medium 48.

The luminous body 40 includes a plurality of linear light sources 44,and a casing 42 containing the light sources 44 therein. The innersurface of the casing 42 has a property of reflecting light, and it maybe additionally given, where necessary, with the function of condensinglight emitted from the light sources 44 toward the forwarding side.

The light transmissive film 405 is constructed similarly to the opticalelement according to one of the above-described embodiments. The lighttransmissive film 405 includes a light incident surface positioned toface the luminous body 40, and a light emergent surface positioned toface the advertising medium 48. On the light incident surface side ofthe light transmissive film 405, spaces having reflecting surfaces arearrayed at a predetermined pitch in the Z-axis direction.

The advertising medium 48 is formed of a film or a sheet having lighttransparency, and it has a surface on which advertising information,including characters, figures, photos, etc., is presented. Theadvertising medium 48 is arranged to be integrated with the luminousbody 40 while covering the light transmissive film 405. When theadvertising medium 48 is illuminated with illumination light that hasbeen emitted from the luminous body 40 and that has passed through thelight transmissive film 405, the advertising information is displayedtoward the front direction.

According to the third modification, since the light transmissive film405 has the function of directionally outputting the light upwards, forexample, it is possible to produce a certain difference in amount oflight passing through the advertising medium 48 between the upwarddirection and the downward direction. Thus, since a desired brightnessdistribution can be given to the advertising medium 48, a decorationeffect of the advertising medium 48 is increased based on the differencein brightness, and visual attractiveness in design of advertisingdisplay can be improved. Further, according to the third modification,since the display light from the advertising medium 48 can be given witha different brightness distribution depending on the viewing direction,viewers can perceive the display and the decoration of the advertisingmedium 48 with feeling different depending on a position, an angle, aheight, etc. to see the advertising medium 48.

Moreover, according to the third modification, the desired brightnessdistribution depending on the information to be displayed by theadvertising medium 48 can be easily given by appropriately changing,e.g., the shape, the array pitch, the width, the depth, and the periodicfeature of the spaces in the light transmissive film 405.

Fourth Modification

The optical element may be applied to not only the illumination device,but also to a fitting (interior member or exterior member) provided witha lighting portion. FIG. 28A is a perspective view illustrating oneexample of the construction of a fitting that includes the opticalelement disposed in a lighting portion. As illustrated in FIG. 28A, afitting 501 includes a lighting member 502 in a lighting portion(region) 504 thereof. In more detail, the fitting 501 includes thelighting member 502 and a frame member 503 that is disposed alongperipheral edges of the lighting member 502. The lighting member 502 isfixedly held by the frame member 503, but it can be removed, whennecessary, by disassembling the frame member 503. One example of thefilling 501 is a shoji (i.e., a paper-made and/or glass-fitted slidingdoor). However, the fitting is not limited to the shoji and can bepracticed in various forms including lighting portions (regions).

FIG. 28B is a sectional view illustrating one example of theconstruction of the lighting member. As illustrated in FIG. 28B, thelighting member 502 includes a base 511 and an optical element 1. Theoptical element 1 is disposed on one of two principal surfaces of thebase 511, which one is positioned on the incident surface side receivingincoming external light (i.e., on the side positioned to face a windowmember). The optical element 1 and the base 511 are joined to each otherwith a joining layer formed of, e.g., a bond layer or an adhesive layerinterposed therebetween. The construction of the lighting member 502 isnot limited to the illustrated one, and the optical element 1 may beitself used as the lighting member 502. As another example of thefitting, a window member disposed in a sash may be constructed similarlyto the optical element.

Other Modifications

While the embodiments have been described, by way of example, asarranging the reflecting surface 151 r to extend in the direction ofthickness of the optical element (i.e., in the X-axis direction), a pairof reflecting surfaces formed by surfaces defining the space on theupper and lower sides thereof are not limited to parallel ones, and theymay be not parallel to each other.

As one example, FIG. 29A illustrates an optical element including astructure layer in which spaces 551A are formed such that the distancebetween the upper and lower surfaces defining each space, which arepositioned to face each other, is continuously reduced from the sidenear the light incident surface S1 toward the side near the lightemergent surface S2. On the other hand, an optical element illustratedin FIG. 29B has a structure in which a space 551Bu providing upper andlower reflecting surfaces both inclined in the +Z-direction from theside near the light incident surface S1 toward the side near the lightemergent surface S2 and a space 551Bd providing upper and lowerreflecting surfaces both inclined in the −Z-direction from the side nearthe light incident surface S1 toward the side near the light emergentsurface S2 are alternately arrayed in the Z-direction. As analternative, at least one of a pair of reflecting surfaces, which areformed by the upper and lower surfaces defining the space, may beinclined with respect to the X-axis. Further, FIG. 29C is a schematicview of an optical element including spaces 551C each of which providesa reflecting surface 551 r inclined at a predetermined inclination angleψ with respect to the X-axis and a reflecting surface parallel to theX-axis direction.

The optical elements illustrated in FIGS. 29A, 29B and 29C are eachfabricated by arranging two light transmissive layers into a stackedstructure as described above with reference to FIGS. 7A to 7C. Morespecifically, the optical elements illustrated in FIGS. 29A and 29C canbe each fabricated by joining a flat light transmissive layer to a lighttransmissive layer including trapezoidal projections formed thereon.Also, the optical element illustrated in FIG. 29B can be fabricated byarranging two light transmissive layers each including trapezoidalprojections formed thereon into such a stacked structure that thetrapezoidal projections of the two light transmissive layers arealternately positioned to leave spaces therebetween.

In addition to the examples illustrated in FIGS. 29A, 29B and 29C, thespaces having the sectional shapes illustrated in FIGS. 8A to 8F andFIGS. 9A to 9F can also be intentionally formed. Those sectional shapescan be obtained, for example, by joining two light transmissive layers,while a force is applied to one of the light transmissive layers in adirection (Z-axis direction) perpendicular to the first direction(X-axis direction), in the manufacturing process described above withreference to FIGS. 7A to 7C.

As described above in the first embodiment, the optical element isdesigned such that the inclination of the reflecting surface and thetilting and/or the curving in shape of the structure layer satisfies theforegoing formula (9). In that case, the inclination angle ψ is definedas an angle formed between a tangential line at an arbitrary point onthe reflecting surface and the X-axis. By designing the optical elementto satisfy the foregoing formula (9), finer control of lightdistribution and more complex light-control function can be realizedwhile the reduction of the upward transmittance is suppressed.

In addition, the multilayer structure of the optical element can beoptionally set, for example, as illustrated in FIGS. 30A to 30F andFIGS. 31A to 31D.

FIG. 30A illustrates an example in which the light transmissive layer 5including the spaces is directly affixed at the bonding layer 7 to thewindow member F. The base 11 may be dispensed with as illustrated inFIG. 30E. FIG. 30B illustrates an example in which the base 11 isattached to the surface of the light transmissive layer 5, which surfaceincludes the spaces formed therein, and the light transmissive layer 5is affixed to the window member F with the base 11 interposedtherebetween. In the example of FIG. 30B, after forming the lighttransmissive layer 5, the light transmissive layer 5 and the base 11 areintegrated by thermal welding, for example. On that occasion, the lighttransmissive layer 5 and the base 11 can be welded to each other in sucha state that no interface exists between both the films. Further, in theexample of FIG. 30B, the bonding layer 7 can be avoided from enteringthe spaces.

FIGS. 30C and 30D illustrate examples in which the light transmissivelayer 5 is affixed to the window member F such that the spaces arepositioned on the light emergent side. That arrangement can also providesimilar advantages to those obtained with the first embodiment. In thearrangement of FIG. 30C, the base 11 may be dispensed with asillustrated in FIG. 30F. In the example of FIG. 30D, a shaped film 611including light diffusing elements, e.g., prisms or crimps, formed onits surface is laminated onto the light emergent side of the lighttransmissive layer 5. The advantageous effect obtained by laminating theshaped film 611 is similar to that described above with reference toFIG. 26.

FIGS. 31A and 31B illustrate examples in which the light transmissivelayer 5 and the base 11 are joined to each with a bonding layer 77having light transparency interposed therebetween. The bonding layer 77can be made of the same type material as that used for the bonding layer7. In the example of FIG. 31A, the light transmissive layer 5 includesthe spaces on the light incident side, and the base 11 is joined to thelight incident side of the light transmissive layer 5. In the example ofFIG. 31B, the light transmissive layer 5 includes the spaces on thelight emergent side, and the base 11 is joined to the light emergentside of the light transmissive layer 5.

FIG. 31C illustrates an example in which the base 11 in FIG. 30A isreplaced with a film 631 having a light diffusing property. FIG. 31Dillustrates an example in which a shaped film 633 having a lightdiffusing property is joined, in the arrangement of FIG. 30B, to thelight emergent side of the light transmissive layer 5. The lightdiffusing function may be given by forming the concave-convex shapedirectly in the light emergent surface of the light transmissive layer 5instead of joining the shaped film 633.

The optical element may further include a hard coat layer from theviewpoint of making the surface of the optical element resistant againstscratching. The hard coat layer is preferably formed on one of the lightincident surface and the light emergent surface of the optical element 1on the side oppositely away from the other surface that is attached toan adherend (attachment target), e.g., a window member. Moreover, theoptical element may include a water-expellant or hydrophilic layer fromthe viewpoint of giving an antifouling property to the light emergentsurface. In addition, the optical element may be used in combinationwith one or more of function layers, such as a heat-ray cutting layer,an ultraviolet cutting layer, and a surface-reflection reducing layer.An adhesive layer and a peeling-off layer may be further stacked ontothe surface of the optical element, which is attached to the adherend,e.g., the window member. The presence of those layers enables theoptical element to be easily attached to the adherend, e.g., the windowmember.

Depending on the use of the optical element, the optical element may becolored to provide a design with visual attractiveness.

While the light incident surface and the light emergent surface of theoptical element are arranged vertically (i.e., in the Z-axis direction),the optical element may be disposed on a horizontal plane or an obliqueplane. In that case, the shape of the space can be adjusted asappropriate so that collected light is output to the desired region. Thelight to be collected is not limited to the sunlight and may beartificial light. Further, the direction in which the light is collectedis not limited to the direction from above, and the light may becollected laterally or from below. Emergent light may be separatelyoutput in plural directions.

It should be understood that various changes and modifications to thepresently preferred embodiments described herein will be apparent tothose skilled in the art. Such changes and modifications can be madewithout departing from the spirit and scope and without diminishing itsintended advantages. It is therefore intended that such changes andmodifications be covered by the appended claims.

1. An optical element comprising: a first surface; a second surfacepositioned to face the first surface; and a plurality of reflectingsurfaces arrayed in a first region defined by the first surface and thesecond surface, wherein the reflecting surfaces have a first length in afirst direction vertical to the first surface and are arrayed at a pitchin a second direction perpendicular to the first direction, lightincident on one of the first surface and the second surface is reflectedby the reflecting surfaces toward the other surface, and followingformulae (1) and (9) are satisfied: $\begin{matrix}{d = {( {{2n} - 1} )\frac{p}{\tan \mspace{2mu} \beta}( {n \in N} )}} & (1) \\{{( {n_{p} + {n_{air}\sin \; \alpha}} )( {n_{p} - {n_{air}\sin \; \alpha}} )\sin^{2}2\psi} \leq {n_{{air}\;}^{2}( {1 - {\cos \; 2{\psi sin}\; \alpha}} )}^{2}} & (9)\end{matrix}$ (where d is the first length, n is a number of totalreflections of the incident light at the same reflecting surface, p isan array pitch of the reflecting surfaces, β is an angle formed betweena projection of the light impinging on the reflecting surface to asurface including the first and second directions and a tangential lineat an arbitrary point on the reflecting surface (6.5°≦β≦87.5°), N is aset of natural numbers, n_(p) is a refractive index inside the regiondefined by the first surface and the second surface, n_(air) is arefractive index of air, α is an incidence angle of the light incidenton the optical element, and ψ is an angle formed in the surfaceincluding the first and second directions between a tangential line atan arbitrary point on the reflecting surface and the first direction).2. An optical element comprising: a first surface; a second surfacepositioned to face the first surface; and a plurality of reflectingsurfaces arrayed in a first region defined by the first surface and thesecond surface, wherein the reflecting surfaces have a curvature in atleast a portion thereof, have a first length in a first directionvertical to the first surface, and are arrayed at a pitch in a seconddirection perpendicular to the first direction, light incident on one ofthe first surface and the second surface is reflected by the reflectingsurfaces toward the other surface, and following formulae (1) and (16)are satisfied: $\begin{matrix}{d = {( {{2n} - 1} )\frac{p}{\tan \; \beta}( {n \in N} )}} & (1) \\{( {\beta + \xi} ) \leq {{Arccos}( {- \frac{n_{air}}{n_{p}}} )}} & (16)\end{matrix}$ (where d is the first length, n is a number of totalreflections of the incident light at the same reflecting surface, p isan array pitch of the reflecting surfaces, β is an angle formed betweena projection of the light impinging on the reflecting surface to asurface including the first and second directions and a tangential lineat an arbitrary point on the reflecting surface) (6.5°≦β≦87.5°), N is aset of natural numbers, np is a refractive index inside the regiondefined by the first surface and the second surface, nair is arefractive index of air, and ξ is an angle of divergence of lightdiverging after being focused, the light impinging on the reflectingsurface, when the portion of the reflecting surface having the curvatureis regarded as a lens).
 3. An optical element comprising: a firstsurface; a second surface positioned to face the first surface; and aplurality of reflecting surfaces arrayed in a first region defined bythe first surface and the second surface, wherein the reflectingsurfaces have fine ruggedness, have a first length in a first directionvertical to the first surface, and are arrayed at a pitch in a seconddirection perpendicular to the first direction, light incident on one ofthe first surface and the second surface is reflected by the reflectingsurfaces toward the other surface, an energy distribution of the lightreflected by the reflecting surfaces is a Gaussian distribution with adirection of specular reflection being a center, a standard deviation ofthe Gaussian distribution is 5° or less, and a following formula (1) issatisfied: $\begin{matrix}{d = {( {{2n} - 1} )\frac{p}{\tan \; \beta}( {n \in N} )}} & (1)\end{matrix}$ (where d is the first length, n is a number of totalreflections of the incident light at the same reflecting surface, p isan array pitch of the reflecting surfaces, β is an angle formed betweena projection of the light impinging on the reflecting surface to asurface including the first and second directions and a tangential lineat an arbitrary point on the reflecting surface) (6.5°≦β≦87.5°), and Nis a set of natural numbers).
 4. The optical element according to claim1, wherein the reflecting surface is formed by an interface between asecond region, which has a second length in the second direction and hasa refractive index differing from the refractive index inside the firstregion, and the first region, and given that the second length is w,(p−w)/p≧0.2 is satisfied.
 5. The optical element according to claim 4,wherein the second region is an air layer.
 6. The optical elementaccording to claim 1, further comprising a structure layer positionedoutside the first region and having a periodic or aperiodicconcave-convex shape with a light diffusing property.
 7. The opticalelement according to claim 6, wherein the concave-convex shape isprovided by prisms having a ridgeline direction aligned with the seconddirection and arrayed at a pitch in a direction perpendicular to boththe first direction and the second direction.
 8. An illumination deviceincluding the optical element according to claim
 1. 9. A window memberincluding the optical element according to claim
 1. 10. A fittingincluding, in a lighting portion thereof, the optical element accordingto claim
 1. 11. A method of manufacturing an optical element, the methodcomprising: transferring a concave-convex shape formed in a master to atransfer material, thereby forming a first light transmissive layer thathas a plurality of reflecting surfaces in a transfer surface thereof;and joining the first light transmissive layer to a second lighttransmissive layer, wherein the reflecting surfaces have a first lengthin a depth direction of the concave-convex shape of the transfer surfaceand are arrayed at a pitch in a second direction perpendicular to thedepth direction of the concave-convex shape, light incident on oneprincipal surface of one of the first light transmissive layer and thesecond light transmissive layer is reflected by the reflecting surfacestoward one principal surface of the other layer, and following formulae(1) and (9) are satisfied: $\begin{matrix}{d = {( {{2n} - 1} )\frac{p}{\tan \; \beta}( {n \in N} )}} & (1) \\{{( {n_{p} + {n_{air}\sin \; \alpha}} )( {n_{p} - {n_{air}\sin \; \alpha}} )\sin^{2}2\psi} \leq {n_{air}^{2}( {1 - {\cos \; 2{\psi s}\; {in}\; \alpha}} )}^{2}} & (9)\end{matrix}$ (where d is the first length, n is a number of totalreflections of the incident light at the same reflecting surface, p isan array pitch of the reflecting surfaces, β is an angle formed betweena projection of the light impinging on the reflecting surface to asurface including the first and second directions and a tangential lineat an arbitrary point on the reflecting surface) (6.5°≦β≦87.5°), N is aset of natural numbers, n_(p) is a refractive index of the first lighttransmissive layer, n_(air) is a refractive index of air, α is anincidence angle of the light incident on the optical element, and ψ isan angle formed in the surface including the first and second directionsbetween a tangential line at an arbitrary point on the reflectingsurface and the first direction).
 12. A method of manufacturing anoptical element, the method comprising: transferring a concave-convexshape formed in a master to a transfer material, thereby forming a firstlight transmissive layer that has a plurality of reflecting surfaces ina transfer surface thereof; and joining the first light transmissivelayer to a second light transmissive layer, wherein the reflectingsurfaces have a curvature in at least a portion thereof, have a firstlength in a depth direction of the concave-convex shape of the transfersurface, and are arrayed at a pitch in a second direction perpendicularto the depth direction of the concave-convex shape, light incident onone principal surface of one of the first light transmissive layer andthe second light transmissive layer is reflected by the reflectingsurfaces toward one principal surface of the other layer, and followingformulae (1) and (16) are satisfied: $\begin{matrix}{d = {( {{2n} - 1} )\frac{p}{\tan \; \beta}( {n \in N} )}} & (1) \\{( {\beta + \xi} ) \leq {{Arccos}( {- \frac{n_{air}}{n_{p}}} )}} & (16)\end{matrix}$ (where d is the first length, n is a number of totalreflections of the incident light at the same reflecting surface, p isan array pitch of the reflecting surfaces, β is an angle formed betweena projection of the light impinging on the reflecting surface to asurface including the first and second directions and a tangential lineat an arbitrary point on the reflecting surface) (6.5°≦β≦87.5°), N is aset of natural numbers, n_(p) is a refractive index of the first lighttransmissive layer, n_(air) is a refractive index of air, and ξ is anangle of divergence of light diverging after being focused, the lightimpinging on the reflecting surface, when the portion of the reflectingsurface having the curvature is regarded as a lens).
 13. A method ofmanufacturing an optical element, the method comprising: transferring aconcave-convex shape formed in a master to a transfer material, therebyforming a first light transmissive layer that has a plurality ofreflecting surfaces in a transfer surface thereof; and joining the firstlight transmissive layer to a second light transmissive layer, whereinthe reflecting surfaces have fine ruggedness, have a first length in adepth direction of the concave-convex shape of the transfer surface, andare arrayed at a pitch in a second direction perpendicular to the depthdirection of the concave-convex shape, light incident on one principalsurface of one of the first light transmissive layer and the secondlight transmissive layer is reflected by the reflecting surfaces towardone principal surface of the other layer, and an energy distribution ofthe light reflected by the reflecting surfaces is a Gaussiandistribution with a direction of specular reflection being a center, astandard deviation of the Gaussian distribution is 5° or less, and afollowing formula (1) is satisfied: $\begin{matrix}{d = {( {{2n} - 1} )\frac{p}{\tan \; \beta}( {n \in N} )}} & (1)\end{matrix}$ where d is the first length, n is a number of totalreflections of the incident light at the same reflecting surface, p isan array pitch of the reflecting surfaces, β is an angle formed betweena projection of the light impinging on the reflecting surface to asurface including the first and second directions and a tangential lineat an arbitrary point on the reflecting surface) (6.5°≦β≦87.5°), and Nis a set of natural numbers).
 14. The method of manufacturing theoptical element according to claim 12, wherein joining the first lighttransmissive layer to a second light transmissive layer includesembedding at least a part of a distal end of a convex portion on thetransfer surface in an adhesive.
 15. The method of manufacturing theoptical element according to claim 12, wherein joining the first lighttransmissive layer to a second light transmissive layer includesswelling a distal end of a convex portion on the transfer surface andpress-bonding the swollen distal end to the second light transmissivelayer such that a shape of the convex portion on the transfer surface ismodified to be closer to a shape as per design values.
 16. The method ofmanufacturing the optical element according to claim 12, wherein joiningthe first light transmissive layer to a second light transmissive layerincludes press-bonding a distal end of a convex portion on the transfersurface to the second light transmissive layer while applying heat tothe distal end of the convex portion on the transfer surface such that ashape of the convex portion on the transfer surface is modified to becloser to a shape as per design values.